# FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD

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< cpp‎ | numeric‎ | fenv

Defined in header `<cfenv>` |  |
#define FE_DOWNWARD /*implementation defined*/ |  | (since C++11)
#define FE_TONEAREST /*implementation defined*/ |  | (since C++11)
#define FE_TOWARDZERO /*implementation defined*/ |  | (since C++11)
#define FE_UPWARD /*implementation defined*/ |  | (since C++11)

Each of these macro constants expands to a nonnegative integer constant expression, which can be used with std::fesetround and std::fegetround to indicate one of the supported floating-point rounding modes. The implementation may define additional rounding mode constants in `<cfenv>`, which should all begin with `FE_` followed by at least one uppercase letter. Each macro is only defined if it is supported.

Constant | Explanation
`FE_DOWNWARD` | rounding towards negative infinity
`FE_TONEAREST` | rounding towards nearest representable value
`FE_TOWARDZERO` | rounding towards zero
`FE_UPWARD` | rounding towards positive infinity

Additional rounding modes may be supported by an implementation.

The current rounding mode affects the following:

- results of floating-point arithmetic operators outside of constant expressions

    double x = 1;
    x / 10; // 0.09999999999999999167332731531132594682276248931884765625
         // or 0.1000000000000000055511151231257827021181583404541015625

- results of standard library mathematical functions

    std::sqrt(2); // 1.41421356237309492343001693370752036571502685546875
               // or 1.4142135623730951454746218587388284504413604736328125

- floating-point to floating-point implicit conversion and casts

    double d = 1 + std::numeric_limits<double>::epsilon();
    float f = d; // 1.00000000000000000000000
              // or 1.00000011920928955078125

- string conversions such as std::strtod or std::printf

    std::stof("0.1"); // 0.0999999940395355224609375
                   // or 0.100000001490116119384765625

- the library rounding functions std::nearbyint, std::rint, std::lrint

    std::lrint(2.1); // 2 or 3

The current rounding mode does NOT affect the following:

- floating-point to integer implicit conversion and casts (always towards zero),
- results of floating-point arithmetic operators in expressions executed at compile time (always to nearest),
- the library functions std::round, std::lround, std::llround, std::ceil, std::floor, std::trunc.

As with any floating-point environment functionality, rounding is only guaranteed if #pragma STDC FENV_ACCESS ON is set.

Compilers that do not support the pragma may offer their own ways to support current rounding mode. For example Clang and GCC have the option `-frounding-math` intended to disable optimizations that would change the meaning of rounding-sensitive code.

### Example

Run this code

    #include <cfenv>
    #include <cmath>
    #include <iomanip>
    #include <iostream>
    #include <string>
    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        std::fesetround(FE_DOWNWARD);
        std::cout << "rounding down: \n" << std::setprecision(50)
                  << "         pi = " << std::acos(-1.f) << '\n'
                  << "stof(\"1.1\") = " << std::stof("1.1") << '\n'
                  << "  rint(2.1) = " << std::rint(2.1) << "\n\n";
        std::fesetround(FE_UPWARD);
        std::cout << "rounding up: \n"
                  << "         pi = " << std::acos(-1.f) << '\n'
                  << "stof(\"1.1\") = " << std::stof("1.1") << '\n'
                  << "  rint(2.1) = " << std::rint(2.1) << '\n';
    }

Output:

    rounding down:
             pi = 3.141592502593994140625
    stof("1.1") = 1.099999904632568359375
      rint(2.1) = 2

    rounding up:
             pi = 3.1415927410125732421875
    stof("1.1") = 1.10000002384185791015625
      rint(2.1) = 3

### See also

float_round_style | indicates floating-point rounding modes (enum)
fegetroundfesetround (C++11)(C++11) | gets or sets rounding direction (function)
C documentation for floating-point rounding macros

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